AFM Images
Bacteria
DNA molecules
Mosquito eye
http://www.afmhelp.com/index.php?option=com_conten
t&view=article&id=51&Itemid=57
Today’s Topic: AFM
(Next Time: FIONA)
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Experimental Approach via Atomic Force Microscopy
AFM: Can see Nanometer & Angstrom scale changes!
How you can see this: Hook’s Law
Imaging Mode, Force Mode.
To minimize noise, go to a higher frequency :
noise always goes like 1/f (f = frequency)
• Force Mode: Worm Like Chain model of Protein
Folding (and DNA)
AFM—Imaging and/or Force
Muller,
Biochemistry, 2008
Imaging – Scan
Ionic
repulsion,
bends tip
Measure (z-axis) distance,
Or
Constant force (by altering
distance with feedback)
http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf
http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&cke
y=1774141&nid=-33986.0.02&id=1774141
AFM—Imaging and/or Force
Force – one place
http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf
http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&cke
y=1774141&nid=-33986.0.02&id=1774141
*
* Regular resolution;
Super-resolution, ~ 10 nm at somewhat greater expense (>$150k)
http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=
eng&ckey=1774141&nid=-33986.0.02&id=1774141
Diff. types of Microscopes
(Diff. l, techniques, diff. resolution)
MBC, Fig. 4-
Or with CCD
1000x, 0.2 um
106x, 2 nm
20,000x 10 nm (3-D)
Transmitted
Light
Resolution of microscope ~l/2, where l is different for different techniques
Hook’s Law and AFM
Imaging—Scan
Force– one place
Ionic
repulsion,
bends tip
Most AFM probes are made from silicon
and/or silicon nitride (Si3N4) wafers using
semiconductor-based etching processes.
Measuring forces
The force is not measured directly, but calculated by measuring the
deflection of the lever, and knowing the stiffness of the cantilever. Hook’s
law gives F = -kz, where F is the force, k is the stiffness of the lever, (in
Newtons/meter) and z is the distance the lever is bent.
Can measure Angstrom resolution – Nobel Prize, 1986
http://cp.literature.agilent.com/litweb/pdf/5990-3293EN.pdf
http://www.home.agilent.com/agilent/editorial.jspx?cc=US&lc=eng&cke
y=1774141&nid=-33986.0.02&id=1774141
What determines how accurately you can measure?
If photodetector was on the moon, could
you see infinitely small changes?
Brownian Noise &
Equipartition Theorem
Each degree of freedom in Energy
goes as x2 or v2 : has ½ kBT of energy.
Examples?
A gas molecule at temperature T:
Kinetic Energy: ½ mv2 : Has ½ kBT of energy
½ mv2 = ½ kT :  v2 = kBT/m  v = √kT/m :
~ 1000 mph!
If you have a spring at finite temperature:
½ kx2 = ½ kBT
AFM Cantilever
How small of a motion can you measure?
z
Bend a cantilever (in z-direction):
½ kz2 = ½ kBT
What is k?
(z2 is the mean square deflection
of the cantilever caused by thermal vibrations)
k= 0.25Ewh3/L3, where E = modulus of Elasticity (Non-trivial but based
(E, how stiff the material is).
on F= kL) --see Joe Howard,
Mechanics of Motor Proteins…
z2 = kBT/k = 0.64Å/√k at 22˚C (where k is in N/m)
k between 0.001 to 100 N/m
(Huge range! Very useful for measuring large range ∆z: F from 1 pN - nN)
Say, 1 N/m = 1 nN/nm: 1 nN causes deviation of 1 nm
1 nN really large for bio0.01 N/m = 10 pN/nm: 1 pN causes a deviation of 1 nm)
Can measure an Angstrom or less!!
Position sensitive detector (PSD)
Out1
P
In1
N
N
In2
P
SIGNAL
Out2
ΔX ~ (In1-In2) / (In1 + In2)
POSITION
Over a fairly wide
range, it’s linear
ΔY ~ (Out1-Out2) /(Out1+Out2)
If tip size is large,
have to worry about distortions
Convolution
Typically, probe radius varies from 5 to 20 nm
http://webserv.jcu.edu/chemistry/faculty/waner/research
/AFM/tipconv.htm
Convolution of tip and sample size
Tobacco Mosaic Virus (TMV)
In truth, diameter of 180 Å.
Due to finite tip size, w~ 350 A
http://webserv.jcu.edu/chemistry/faculty/waner/research/AFM/tipconv.htm
Correlation functions
Cross-correlation
Cross-correlation
http://www.scholarpedia.org/article/1/f_noise
The End